Question

find the area isocles triangle?​

Answer 1

Answer:

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Step-by-step explanation:

Derivation for Isosceles Triangle Area Using Heron’s Formula

The area of an isosceles triangle can be easily derived using Heron’s formula as explained below.

According to Heron’s formula,

Area = √[s(s−a)(s−b)(s−c)]

Where, s = ½(a + b + c)

Now, for an isosceles triangle,

s = ½(a + a + b)

⇒ s = ½(2a + b)

Or, s = a + (b/2)

Now,

Area = √[s(s−a)(s−b)(s−c)]

Or, Area = √[s (s−a)2 (s−b)]

⇒ Area = (s−a) × √[s (s−b)]

Substituting the value of “s”

⇒ Area = (a + b/2 − a) × √[(a + b/2) × ((a + b/2) − b)]

⇒ Area = b/2 × √[(a + b/2) × (a − b/2)]

Or, area of isosceles triangle = b/2 × √(a2 − b2/4)

Area of Isosceles Right Triangle Formula

The formula for Isosceles Right Triangle Area= ½ × a2

Derivation:

Area of isosceles triangle formula

Area = ½ ×base × height

area = ½ × a × a = a2/2

Perimeter of Isosceles Right Triangle Formula

P = a(2+√2)

Derivation:

The perimeter of an isosceles right triangle is the sum of all the sides of an isosceles right triangle.

Suppose the two equal sides are a. Using Pythagoras theorem the unequal side is found to be a√2.

Hence, perimeter of isosceles right triangle = a+a+a√2

= 2a+a√2

= a(2+√2)

= a(2+√2)

Area of Isosceles Triangle Using Trigonometry

Using Length of 2 Sides and Angle Between Them

A = ½ × b × c × sin(α)

Using 2 Angles and Length Between Them

A = [c2×sin(β)×sin(α)/ 2×sin(2π−α−β)]

Answer 2

Step-by-step explanation:

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